The conventional method to detect the intersubband resonance in a bulk SE sample containing about \(10^8\)  electrons is to observe the corresponding change in the transmitted power of the resonant microwave (MW) radiation due to its absorption by the excited electrons [1]}, [2]}. For the typical density of electrons \(n_s\sim 10^8\)  cm\(^{-2}\) , a single microchannel employed in our experiment would contain on the order of \(10^3\)  electrons, which makes the microwave absorption detection impossible. A new method of the Rydberg resonance detection was developed recently, which is based on the measurement of the image-current induced by the excited SE in a conducting electrode capacitively coupled to the electrons [3]}. While it was argued that this method can be potentially scaled down to the detection of the Rydberg excitation of a single electron, the currently achieved sensitivity of this method was not sufficient to detect the resonance in the experiment reported here. As an alternative, we used the conductive detection of the Rydberg resonance by observing a change in the current of SE driven along the microchannel, which is induced by the heating of electrons due to the resonant MW absorption [4]}, [5]}. In particular, in order to increase sensitivity of the conductive detection we employed SE in a crystalline state to exploit a large change in the conductivity of SE upon their transition from the solid to the liquid phase.
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